Exposure to chemical mixtures is the rule rather than the exception. Examples include diet, pharmaceutical agents and air pollution. In public health, is deemed important to develop statistical methods for estimating the toxicity of a complex mixture. By identifying the toxicity of some specific agents in the mixture, we will guide the development of hypotheses on biological mechanisms of action that can be tested in experimental models and we will better inform public policy. We have assembled national datasets on health outcomes, chemical components of PM10 (particulate matter 10m) and confounders. PM10 can be viewed as a mixture represented by a hierarchically structured predictor characterized by two PM sizes (PM2:5 and PM102:5), more than fifty chemical constituents of PM2:5, and groups of chemical constituents that have the same chemical characteristics (see Figure 1 left and center panels). Motivated by this scientific problem, we propose to develop: A.1) a novel class of Bayesian hierarchical models with an imprecise hierarchically structured predictor; A.2) innovative Bayesian methods to account for adjustment uncertainty in effect estimation; A.3)new methods for checking regression models for data in space and time by decomposing exposure effect estimates into components associated with distinct spatio-temporal scales of variation that should be the same when the model specification is correct. We will apply methods to national databases of air pollution, weather, and health for estimating the toxicity of the PM mixture on a national scale (A.4). The ability to make scientific findings reproducible is increasingly important in areas where substantive results are the product of complex statistical computations. In A.5, we will develop computational tools for disseminating data, statistical methods, and scientific results. Our methods and associated computational tools will advance statistical and computational methods for population health studies of exposure to chemical mixtures. The methods developed here will provide a general platform for dealing with complex mixtures and can be applied to other biological questions, for example, to identify putative disease genes that are organized by functional pathways or other prior hypotheses. PUBLIC HEALTH RELEVANCE: Exposure to chemical mixtures is the rule rather than the exception, diet, pharmaceutical agents and air pollution are common examples. In this proposal we will develop a novel class of statistical models for estimating adverse health effects associated with exposure to chemical mixtures. By identifying the toxicity of some specific agents in the mixture, we will guide the development of hypotheses on biological mechanisms of action that can be tested in experimental models and we will better inform public policy.